After solving a matrix you will have either zero, one, or an infinite number of solutions. For example the solution [tex]x_{1}=0[/tex] [tex] x_2=0[/tex] [tex] x_3=0[/tex] might be the solution set to a homogeneous system. Once you get the matrix to reduced row form the solution set should be apparent just from looking at the matrix.

Well that particular matrix will have an infinite number of solutions because you have more unknowns than equations. The matrix is already reduced as much as possible I believe. In this situation you would generally introduce one or more parameters and back substitute.

For example according to your matrix [tex]x_4=5+x_5[/tex] and [tex]x_3=15+5x_5[/tex] and [tex]x_1=11+3x_5-2x_2[/tex].

If you set [tex]x_5=t[/tex] and [tex]x_2=s[/tex] you should be able to solve for each variable in terms of s and t.